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Risk-adjusted return on equity compares an approved measure of risk-adjusted profit with allocated equity. Work through a bank business-unit comparison, reconcile the adjustments and see how capital allocation changes the answer.
Risk adjusted return on equity measures approved risk-adjusted profit relative to the equity allocated to a bank business unit. It helps compare earnings after the bank's stated risk adjustments, rather than ranking units by accounting profit alone. The formula is simple; the definitions supplied by finance, risk and capital management determine what the result means.
Risk-adjusted return on equity = After-tax risk-adjusted profit / Average allocated equity
Use annual profit with average equity allocated during that year. If the bank instead uses a period-end allocation or a different capital base, label it explicitly and apply it consistently.
There is no reason to assume that every bank uses the same numerator or denominator. The Basel Committee's review of economic-capital frameworks describes economic capital as methods for assessing risk and assigning capital, while emphasizing methodological and implementation challenges. Economic capital supplied by an approved bank framework is an input; an article's worked ratio is not an estimate of that capital.
The convention below is deliberately specific. A fictional US bank replaces the accounting credit-loss expense in business-unit profit with its approved expected-loss charge. Funding and operating costs remain unchanged, and a common tax assumption converts adjusted pretax profit to after-tax profit. The denominator is average allocated equity supplied by capital management.
This is different from adjusted return on equity, which addresses profit normalization. It is also different from return on tangible equity, which changes the equity base for stated intangible-asset adjustments.
Use one row per business unit and reporting period, with these fields:
| Input | File or owner | Consistency check |
|---|---|---|
| Revenue | Business-unit income statement | Same period and consolidation scope |
| Funding cost | Approved internal funding allocation | Same funding convention across units |
| Operating cost | Cost allocation workbook | Shared expenses included consistently |
| Accounting credit-loss expense | Unit ledger reconciliation | Exactly the expense being replaced |
| Approved expected-loss charge | Risk-approved input file | Same horizon and definition across units |
| Tax assumption | Finance-approved schedule | Applied to the stated adjusted profit basis |
| Average allocated equity | Capital-management schedule | Same averaging dates and allocation version |
| Return hurdle | Approved performance policy | Same tax and capital basis as the ratio |
Include the input version and approval date in the working file. A change in allocation policy can change unit returns without any customer or expense changing.
Capital allocation has a broader purpose than maximizing a performance ratio. The Federal Reserve's SR 15-18 guidance, which applies to Category I firms, explains that capital absorbs unexpected losses and supports continued lending. It also identifies governance, risk management and internal controls as capital-planning expectations. Do not treat this comparison as regulatory approval or a capital-adequacy test.
The bank compares corporate lending and commercial real estate for one full year. All source amounts are USD. The supplied tax assumption is 25%, and allocated equity is already averaged over the year.
| Annual input (USD) | Corporate lending | Commercial real estate | Total |
|---|---|---|---|
| Revenue | 12,000,000 | 11,000,000 | 23,000,000 |
| Funding cost | 4,000,000 | 4,000,000 | 8,000,000 |
| Operating cost | 3,000,000 | 2,500,000 | 5,500,000 |
| Accounting credit-loss expense | 1,500,000 | 500,000 | 2,000,000 |
| Accounting pretax profit | 3,500,000 | 4,000,000 | 7,500,000 |
| Approved expected-loss charge | 1,000,000 | 1,500,000 | 2,500,000 |
| Average allocated equity | 20,000,000 | 25,000,000 | 45,000,000 |
Accounting pretax profit is revenue less funding cost, operating cost and accounting credit-loss expense. Replace the last expense as follows:
Risk-adjusted pretax profit = Accounting pretax profit + Replaced accounting credit-loss expense − Approved expected-loss charge
After-tax risk-adjusted profit = Risk-adjusted pretax profit × (1 − Tax rate)
| Calculation | Corporate lending | Commercial real estate | Total |
|---|---|---|---|
| Accounting pretax profit (USD) | 3,500,000 | 4,000,000 | 7,500,000 |
| Add back replaced expense (USD) | 1,500,000 | 500,000 | 2,000,000 |
| Deduct expected-loss charge (USD) | −1,000,000 | −1,500,000 | −2,500,000 |
| Risk-adjusted pretax profit (USD) | 4,000,000 | 3,000,000 | 7,000,000 |
| Tax at 25% (USD) | 1,000,000 | 750,000 | 1,750,000 |
| After-tax risk-adjusted profit (USD) | 3,000,000 | 2,250,000 | 5,250,000 |
| Average allocated equity (USD) | 20,000,000 | 25,000,000 | 45,000,000 |
| Risk-adjusted return on equity | 15.00% | 9.00% | 11.67% |
Percentages are rounded to two decimal places after calculation. The combined result is 5,250,000 / 45,000,000 = 11.67%. It is not the simple average of the two unit returns, which is 12.00%.
If the two adjusted profits occupy F2:F3 and allocated equity occupies G2:G3, the combined ratio is:
=SUM(F2:F3)/SUM(G2:G3)
The commercial real estate unit reported more accounting pretax profit. Under the stated expected-loss convention, corporate lending produces more risk-adjusted profit while using less allocated equity. That is the comparison the accounting ranking alone misses.
First reconcile total adjusted profit back to the accounting inputs:
7,500,000 + 2,000,000 - 2,500,000 = 7,000,000 pretax
7,000,000 - 1,750,000 = 5,250,000 after tax
Then prove that the unit results reproduce the total:
(20,000,000*15% + 25,000,000*9%)/45,000,000 = 11.67%
Use the unrounded underlying ratios for the check. Allocations and adjustments must tie to their approved schedules, including any corporate or unallocated balance excluded from these two units.
Suppose the bank supplies a 10% after-tax hurdle on the same allocated-equity basis. This is an example assumption, not an industry benchmark.
| Hurdle test | Corporate lending | Commercial real estate | Total |
|---|---|---|---|
| Equity charge at 10% (USD) | 2,000,000 | 2,500,000 | 4,500,000 |
| After-tax risk-adjusted profit (USD) | 3,000,000 | 2,250,000 | 5,250,000 |
| Profit above equity charge (USD) | 1,000,000 | −250,000 | 750,000 |
The negative amount prompts a review of pricing, expenses, risk charges or the capital allocation. It does not establish which one should change. Business leaders own the commercial response; finance owns reconciliation, risk owns the approved risk inputs, and capital management owns the equity allocation.
Hold corporate lending's $3,000,000 adjusted profit constant but increase its allocated equity from $20,000,000 to $25,000,000. Its return becomes 12.00%, down from 15.00%. Combined equity becomes $50,000,000, so the two-unit return falls to 5,250,000 / 50,000,000 = 10.50%.
No earnings changed. The lower return reflects a larger denominator. Keep this effect separate from profit deterioration, and use return on equity by industry only for comparisons with compatible definitions and business scope.
Bring the business-unit profit workbook, approved risk adjustments and allocated-equity schedule. Covirage maps the columns, and its tools compute and check the return comparison; the external AI model explains the results with every figure traced to its rows. Create a free Covirage account, then set up your business and bring a sample of your own data.
See Covirage for commercial banking for the supporting context.
Names vary across institutions. Some frameworks use economic capital, while others use allocated equity or another approved capital measure. Compare the documented numerator and denominator rather than treating the acronym as a complete definition. Two measures with different capital bases may rank the same units differently.
Check the approved policy first. If reported income already includes a credit-loss expense that the framework replaces with expected loss, add back the replaced expense before deducting expected loss. Deducting both without an explicit reason charges the unit twice for the same risk adjustment.
The return alone cannot determine the appropriate allocation. A lower denominator mechanically raises the ratio, even with unchanged earnings. Risk and capital owners must approve the allocation and assess its adequacy; the performance comparison only shows the consequences of the supplied inputs.
Ordinary adjusted ROE typically removes specified accounting items to compare underlying earnings. Risk-adjusted ROE applies an institution's risk and capital conventions. Removing a restructuring charge does not by itself adjust for credit, market or operational risk, so label the two measures separately.